Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models |
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Authors: | Wolfgang Lucha Dmitri Melikhov Silvano Simula |
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Institution: | 1. HEPHY, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna, Austria;2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria;3. SINP, Moscow State University, 119991 Moscow, Russia;4. INFN, Sezione di Roma III, Via della Vasca Navale 84, I-00146 Roma, Italy |
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Abstract: | We compare the extraction of the ground-state decay constant from the two-point correlator in QCD and in potential models and show that the results obtained at each step of the extraction procedure follow a very similar pattern. We prove that allowing for a Borel-parameter-dependent effective continuum threshold yields two essential improvements compared to employing a Borel-parameter-independent quantity: (i) It reduces considerably the (unphysical) dependence of the extracted bound-state mass and the decay constant on the Borel parameter. (ii) In a potential model, where the actual value of the decay constant is known from the Schrödinger equation, a Borel-parameter-dependent threshold leads to an improvement of the accuracy of the extraction procedure. Our findings suggest that in QCD a Borel-parameter-dependent threshold leads to a more reliable and accurate determination of bound-state characteristics by the method of sum rules. |
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